2020/09/21 by Ezéchiel Kahn, Kahn, Ezechiel · 1 citation
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2009.09874
openalex publication_date 2020/09/21 · openalex created_date 2020/09/25 · openalex updated_date 2026/07/28
This paper is devoted to the study of the eigenvalues of the Wishart process which are the analogof the Dyson Brownian Motion for covariance matrices. Such processes were in particular studied byBru. The mean field convergence of the empirical measure of these eigenvalues was proved Malecki andPerez. In this paper, we provide a new approach to the mean field convergence problem using toolsfrom the free rectangular convolution theory developed by Benaych-Georges, which in particular allowsto compute explicitly the limit measure valued flow. We highlight the link with the integro-differentialequation related to the mean field limit and its translation into a complex Burgers partial differentialequation.